When \(U=-M_0=-27\)  meV is fixed (\(E_z\simeq -0.5\)  V/nm [1]}), our results of MR ratio versus \(E_{\rm F}\)  in Fig. 2(a) show that nearly-perfect MR effect, i.e. \(|\rho _{\rm R}|\simeq 100\%\) , appears for \(|E_{\rm F}|/M_0\in (0.5,1.5)\) , independent of whether the DW is present or not. The MR ratio of this spin valve effect changes the sign if a DW appears. This is because the \(m_z\) -induced spin polarization near \(E_{\rm F}\)  changes sign in terminal R (is unchanged in L). Nontrivially, we find the giant MR effect is not sensitive to whether the DW type is collinear, Bloch or Néel, and meanwhile, the spin valve effect is irrelevant to the magnetic chirality of DW, confirmed by changing the sign of \(m_x\)  or \(m_y\)  in calculations. To illustrate the MR effect in more detail, we show the contour plot of MR ratio in the \((E_{\rm F},U)\)  plane for the collinear DW in Fig. 2(b). The result shows that there is a sharp transition between the absence of the MR effect for lower \(E_{\rm F}\)  and the nearly-perfect MR effect for higher \(E_{\rm F}\)  [see also \(|E_{\rm F}|/M_0<0.5\)  in Fig. 2(a)]. This parameter regime of no MR, \(G_{\rm P(AP)}\equiv 0\) , is attributed to either of the following two factors: One is the absence of transport states induced by band gap in two terminals, and the other is the spin mismatch for both P and AP bias configurations.
